Q. 45.0( 1 Vote )

Using determinants prove that the points (a, b) (a’, b’) and (a – a’, b – b’) are collinear if ab’ = a’b.

Answer :

Given: – (a, b) (a’, b’) and (a – a’, b – b’) are points and ab’ = a’b


To Prove: – (a, b) (a’, b’) and (a – a’, b – b’) are collinear points


Proof:


Tip: – If three points to be collinear, then the area of the triangle formed by these points will be zero.


Now, we know that,


vertices of a triangle are (x1,y1), (x2,y2) and (x3,y3), then the area of the triangle is given by:



Thus



Expanding along R1





ab – ab = 0


ab = ab


Hence, Proved.


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